Mathematical Models of Biological Systems

Hugo van den Berg

Discusses how to develop, solve, and interpret mathematical models, starting from first principles and working through increasingly complex case studies

Incorporates a range of biologically relevant examples from fields as diverse as ecology, epidemiology, and physiology

Emphasizes the crucial importance of care and accuracy in dealing with parameters such as dimensional analysis, measurement scales, and mathematical quantities

Based on a proven course structure

Mathematical Models of Biological Systems

Hugo van den Berg

Description

Mathematical Models of Biological Systems provides a practical introduction to basic mathematical modelling methodology and analysis. It covers a variety of biological applications and uses these topics in turn to highlight key components in the art of modelling. Its primary aim is to give students the tools to translate simple, real-world biological problems into rigorous mathematical models. A secondary aim is to teach the reader how to critically assess the modelling components in the primary life science literature.

The book covers deterministic as well as stochastic dynamics, continuous-time as well as discrete-time dynamics, partial differential equations, dimensional analysis, and curve fitting/parameter estimation. It contains numerous case studies, graded from elementary examples to more complicated problems, as well as a general treatment of good modelling practice. Although the book assumes a basic background in mathematics, specifically beginning calculus and elementary statistics, all requisite material is included in a series of appendices.

Mathematical Models of Biological Systems

Hugo van den Berg

Table of Contents

Preface1. What models can do for the life sciences2. Basic modelling concepts and techniques3. Working with Ordinary Differential Equations4. Models and data analysis5. Modelling principles6. Growth of populations and of individuals7. Infection and immunity8. Physiology9. Stochastic modelsAppendix A: Maths miscellanyAppendix B: From Boltzmann to NernstAppendix C: Ultimate behaviour of a closed, connected, compartmental systemAppendix D: Buckingham's theoremAppendix E: Minimising the sum of squares with respect to the parametersAppendix F: Global sensitivity analysis: parameter transformations for 'large' systemsIndex

Mathematical Models of Biological Systems

Hugo van den Berg

Author Information

Hugo van den Berg obtained an MSc in neurophysiology and molecular endocrinology from the Free University of Amsterdam and a PhD in theoretical ecology from the same university. He became a Research Fellow and later a lecturer in Mathematical Biology at the University of Warwick. His chief research interests are specificity of immune recognition, nutrient fluxes, energy balance in individuals and ecosystems, regulation of contractions in childbirth, and receptor signalling.

Mathematical Models of Biological Systems

Hugo van den Berg

Reviews and Awards

Mathematical Models of Biological Systems was featured in The Quarterly Review of Biology.